The Kansas City Chiefs overwhelmed the Indianapolis Colts for a 31-13 win in the divisional round of the NFL playoffs on Saturday.

Through snow at Kansas City’s Arrowhead Stadium, Chiefs’ quarterback Patrick Mahomes threw for 278 yards on 27 of 41 passing. Kansas City ran for 180 yards and four touchdowns, with running back Damien Williams leading the way with 129 yards and a touchdown on 25 carries.

The Chiefs’ defense, once considered a liability, was stifling. Until the final drive of the first half, the Colts did not convert an offensive first down. By the end of the game, they were outgained, 433 yards to 263. Kansas City ran 25 more plays. The Colts were 0 for 9 on third downs.

The Chiefs will advance to host the winner of the Sunday’s Patriots-Chargers matchup in the AFC championship game. The win marks Kansas City’s first home playoff victory since 1991.

Here are the three biggest takeaways from the Chiefs' dominant win:

With help from the Chiefs’ defense, the Colts’ offense disappeared

The Colts’ offense, which wowed the league last week against Houston, melted against the Kansas City defense. Andrew Luck, his shoulder finally healthy, was a revelation for Indianapolis in the wild card round, but the Chiefs defense pestered him into 19-of-36 passing for 203 yards on Saturday. T.Y. Hilton, expected to pose problems for an undermanned Kansas City secondary, only caught four passes for 60 yards, and two of those catches (including a touchdown) came when the game was well in hand. Running back Marlon Mack, who excelled last week versus Houston, didn’t top 50 yards rushing.

That’s all thanks to a Chiefs' defense that played with the tenacity of a team that thinks it is playing out its destiny. Rushing off the edge, Dee Ford found success all game against the Indianapolis offensive line. When the Colts recovered a Chiefs fumble at the Kansas City 20-yard line, giving them a chance to come back in the game, Ford broke free on a pass rush and stripped the ball from Luck’s hand, and Justin Houston scooped up the loose ball.

Every time the Colts made a push on offense, which ranked fifth in the NFL this season in points per game, the Chiefs’ defense was there to answer.

It was the Chiefs’ running game that made the difference on offense

Kansas City scored four rushing touchdowns Saturday, with four different players. Damien Williams led all rushers with 129 yards on 25 carries. Before Saturday, he only had five games with double-digit rushing attempts, and none with more than 13. The Chiefs' second touchdown came on a 36-yard pitch to wide receiver Tyreek Hill. Mahomes scrambled for a 4-yard score. Darrel Williams iced the game with a 6-yard touchdown run.

The Chiefs’ running game allowed them to control the clock and field position and hit big plays on any given snap. It’s worth marveling at their ground game, and not just Mahomes’s magic through the air.

That was very un-Vinatieri-like

Indianapolis would certainly like to have the four points kicker Adam Vinatieri left on the field. The Colts drove 70 yards in eight plays to end the second quarter. Their offense was finally clicking, after Luck got into a rhythm running a no-huddle set. He led Indianapolis down to the Chiefs' 5-yard line, where a Vinatieri chip-shot would have made it a two-score game at the half. That wasn’t a bad outcome, given how poorly Indianapolis had played to that point.

But Vinatieri doinked the kick off the left upright. It was the shortest missed field goal of his career. In the second half, he pushed an extra point wide to the right, his first missed extra point in the playoffs in his 23-year career. The Colts got beaten thoroughly on both offense and defense, but a little help from Vinatieri would have made a comeback attempt just a little easier, and possibly applied a little more pressure on Kansas City.

Key plays:

Chiefs get one for the road: As if Kansas City wasn’t dominant enough Saturday evening, the Chiefs added another touchdown late to seal the game. Darrel Williams powered his way through the Colts' defense for a six-yard scoring run, helped along the way by a shove in the back from Patrick Mahomes. The Chiefs’s drive stay alive after a running into the punter penalty by Indianapolis. (31-13, Kansas City, 2:23 fourth quarter)

Touchdown, Colts: Indianapolis still has a little life left. Andrew Luck connected with T.Y. Hilton for a 29-yard score to keep the Colts alive, barely. It doesn’t help that Adam Vinatieri missed the extra point, his second missed kick of the game. (24-13, Kansas City, 3:51 fourth quarter)

Colts and Chiefs trade fumbles: Just as Indianapolis looked to have some momentum going its way, the Chiefs took it right back. Kansas City’s Sammy Watkins took a pass and ran out wide, but Colts star rookie linebacker Darius Leonard forced the ball from Watkins' hands at the Kansas City 20-yard line with a minute to play in the third quarter and recovered the fumble. But two plays later, Chiefs' edge rusher Dee Ford knocked the ball out of Andrew Luck’s hands and Justin Houston pounced on the loose ball for Kansas City. (24-7, Kansas City, start fourth quarter)

Chiefs answer: Patrick Mahomes’s knee appears to be just fine. He capped a 10-play, 75-yard drive with a four-yard touchdown scramble and dive to the pylon. Kansas City has thoroughly dominating the Colts on both sides of the ball. The Chiefs have 16 first downs, while the Colts had none before their final drive. The Chiefs have 274 total yards so far. (24-7, Kansas City, 1:40 second quarter)

Touchdown, Colts: Indianapolis’s Najee Goode came right through the middle of the Chiefs' punt formation and stuffed Dustin Colquitt’s punt, then Zach Pascal recovered it in the end zone for a touchdown. The Colts are on the board, but still don’t have a first down on offense. (17-7, Kansas City, 5:56 second quarter)

Chiefs eyeing an early blowout: Kansas City’s offense was able to move the ball very effectively in the first quarter. The Chiefs produced 185 yards of total offense, including 112 for Patrick Mahomes on 8-of-14 attempts. They start the second quarter with a second-and-8 and the Colts' 29-yard line. (14-0, Kansas City, start second quarter)

Chiefs Drives

Colts Drives

Touchdown — 5 plays, 90 yards

Punt — 3 plays, 7 yards

Touchdown — 8 plays, 70 yards

Punt — 3 plays, 0 yards

Field goal — 14 plays, 53 yards

Punt — 3 plays, 5 yards

Chiefs strike first: The snow doesn’t seem to be bothering Kansas City’s offense. Patrick Mahomes is 3-for-3 through the air already for 61 yards and Damien Williams chugged in from 10 yards out for a score on the Chiefs' first drive. (7-0, Kansas City, 10:05 first quarter)